The LAE fractions for our sample were calculated with \(EW(\mbox{Ly$\alpha $})_{\rm emi.}\)  in a similar method in that of [1]} using the MUSE-HUDF data, which cannot take \(\mbox{Ly$\alpha $}\)  absorption into account as their continua are not detected in the MUSE spectra (i.e., nondetection of absorption) for most of the sources. \(\mbox{Ly$\alpha $}\)  fluxes from extended emission were not included in the \(EW(\mbox{Ly$\alpha $})\)  for both samples. We did not correct the incompleteness of the detection of \(\mbox{Ly$\alpha $}\)  emission for our sample as the completeness is expected to be high, and we estimated the uncertainties on the \(X_{\rm LAE}\)  from the binomial proportion confidence interval. The \(X_{\rm LAE}\)  with the typical threshold for LAE selections, \(EW(\mbox{Ly$\alpha $})\ge 20\)  Å, for out entire sample with \(-20\le M_{1500}\le -18.0\)  at \(z=2.9\) –\(4.4\)  is \(0.33^{+0.11}_{-0.09}\) . For a fair comparison, we also calculated the \(X_{\rm LAE}\)  with \(EW(\mbox{Ly$\alpha $})\ge 65\)  Å for our entire sample as \(0.14^{+0.09}_{-0.06}\) . As discussed in Section REF , this value is similar to those in [1]}, suggesting that our sample is not biased.
